7x(8x-1)(3x-5)=0

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Solution for 7x(8x-1)(3x-5)=0 equation: 


Simplifying
7x(8x + -1)(3x + -5) = 0

Reorder the terms:
7x(-1 + 8x)(3x + -5) = 0

Reorder the terms:
7x(-1 + 8x)(-5 + 3x) = 0

Multiply (-1 + 8x) * (-5 + 3x)
7x(-1(-5 + 3x) + 8x * (-5 + 3x)) = 0
7x((-5 * -1 + 3x * -1) + 8x * (-5 + 3x)) = 0
7x((5 + -3x) + 8x * (-5 + 3x)) = 0
7x(5 + -3x + (-5 * 8x + 3x * 8x)) = 0
7x(5 + -3x + (-40x + 24x2)) = 0

Combine like terms: -3x + -40x = -43x
7x(5 + -43x + 24x2) = 0
(5 * 7x + -43x * 7x + 24x2 * 7x) = 0
(35x + -301x2 + 168x3) = 0

Solving
35x + -301x2 + 168x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(5 + -43x + 24x2) = 0

Factor a trinomial.
7x((1 + -8x)(5 + -3x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve:

Simplifying
1 + -8x = 0

Solving
1 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x = 0 + -1
-8x = 0 + -1

Combine like terms: 0 + -1 = -1
-8x = -1

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, 0.125, 1.666666667}

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